Blitz the pineapple in a food processor or with a hand blender until smooth.
Scrape the pineapple into a medium bowl and stir in the yoghurt, agave syrup, lime zest, coconut rum and single cream alternative until smooth.
Scrape into a plastic freezer-proof container and put the lid on. Place in the freezer for 1½ hours, until beginning to freeze around the edges.
Remove from the freezer and scrape the frozen edges into the centre and stir. Use an electric handheld whisk to whisk the ice cream for about a minute, until smooth. This is to break up the ice crystals and give the ice cream a smooth texture. Alternatively, use a balloon whisk.
Replace the lid and return to the freezer.
Freeze for 1 hour, until the ice cream is freezing around the edges.
Remove from the freezer and scrape the frozen edges into the centre and stir. Use an electric handheld whisk to whisk the ice cream for about a minute, until smooth.
Replace the lid and return to the freezer. Freeze for about 5 hours, or until frozen completely.
Remove the ice cream from the freezer 15-20 minutes before serving. This will allow it to soften and make it easier to scoop out.
Serve decorated with a slice of lime and a small piece of pineapple.